Wild boundary behaviour of homomorphic functions in domains of C^N

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2021-01-01 DOI:10.1512/iumj.2021.70.8749

S. Charpentier, L. Kosinski

引用次数: 8

Abstract

Given a domain of holomorphy D in C , N ≥ 2, we show that the set of holomorphic functions in D whose cluster sets along any finite length paths to the boundary of D is maximal, is residual, densely lineable and spaceable in the spaceO(D) of holomorphic functions in D. Besides, if D is a strictly pseudoconvex domain in C , and if a suitable family of smooth curves γ(x, r), x ∈ bD, r ∈ [0, 1), ending at a point of bD is given, then we exhibit a spaceable, densely lineable and residual subset of O(D), every element f of which satisfies the following property: For any measurable function h on bD, there exists a sequence (rn)n ∈ [0, 1) tending to 1, such that f ◦ γ(x, rn)→ h(x), n→∞, for almost every x in bD.

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C^N域上同态函数的野边界行为

给定一个域正则D C, N≥2,我们表明,在D组全纯函数的集群在任何有限长度的路径设置为D是最大的边界,是残留,密集lineable和spaceable spaceO (D)的全纯函数D。此外,如果D是一个严格伪凸域在C语言中,如果一个合适的家庭光滑曲线γ(x, r), x∈bD, r∈(0,1),结束点的双相障碍,然后我们spaceable展览,O(D)的可密列残差子集，其每个元素f满足以下性质:对于bD上的任意可测函数h，存在一个序列(rn)n∈[0,1]趋于1，使得f◦γ(x, rn)→h(x)， n→∞，对于bD中的几乎每一个x。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.